Sparse sampling and reconstruction for electron and scanning probe microscope imaging

ABSTRACT

Systems and methods for conducting electron or scanning probe microscopy are provided herein. In a general embodiment, the systems and methods for conducting electron or scanning probe microscopy with an undersampled data set include: driving an electron beam or probe to scan across a sample and visit a subset of pixel locations of the sample that are randomly or pseudo-randomly designated; determining actual pixel locations on the sample that are visited by the electron beam or probe; and processing data collected by detectors from the visits of the electron beam or probe at the actual pixel locations and recovering a reconstructed image of the sample.

RELATED APPLICATION

This application claims priority to United States Provisional PatentApplication No. 61/877,109, filed on Sep. 12, 2013, and entitled “SPARSESAMPLING AND RECONSTRUCTION FOR SCANNING ELECTRON MICROSCOPE IMAGING”,the entirety of which is incorporated herein by reference.

STATEMENT OF GOVERNMENTAL INTEREST

This invention was made with Government support under Contract No.DE-AC04-94AL85000 between Sandia Corporation and the U.S. Department ofEnergy. The Government has certain rights in the invention.

BACKGROUND

Electron microscopes are used in neuroscience, microbiology andmaterials science for high-resolution imaging and subsequent structuralor compositional analysis. In particular, many applications that utilizea scanning electron microscope (SEM) require imaging millimeters or evencentimeters of material at nanometer resolutions, leading tosemi-autonomous operation of the SEM, weeks of around-the-clockcollection time, and vast quantities of data. Scanning probe microscopesare similarly limited.

A traditional SEM operates in raster mode, visiting every “pixel”location in sequence. Many engineering advances have been proposed toincrease the speed of raster mode through faster scanning coils, orefficiency gains through image acquisition buffers and communicationsprotocols. Nevertheless, there is a need to provide faster scan times.Advancements that provide speedup in series with any of theaforementioned engineering advances would be particularly beneficial.

Interpolation methods of sampling and imaging, such as bilinearinterpolation, are known, but are difficult to apply in high noiseenvironments. A structured sampling methodology, such as interpolation,may also miss details that are regularly structured in a way that avoidsrecognition of the structure of the sample.

SUMMARY

Systems and methods for electron and scanning probe microscope imagingare provided herein. In a general embodiment, the present disclosureprovides a method for conducting electron or scanning probe microscopy.The method comprises driving an electron beam or probe to scan across asample and visit a subset of pixel locations of the sample that arerandomly or pseudo-randomly designated; determining actual pixellocations on the sample that are visited by the electron beam or probe;and processing data collected by detectors from the visits of theelectron beam or probe at the actual pixel locations and recovering areconstructed image of the sample.

In another embodiment, the present disclosure provides a retrofit toexisting scanning probe or electron microscopes to speed up imageacquisition by about two times or greater while providing “smooth”images in which the electron probe measures one-at-a-time arandomly-selected subset of the pixel locations. Smooth images havefeatures that are relatively few and large compared to the pixelspacing. Smooth images are highly compressible. This solution may beparticularly desirable in very long collections, such as those needed inbiology, neuroscience and materials science.

In an embodiment, image reconstruction is performed using a compressivesensing inversion method/split Bergman method that utilizes a totalvariation prior. Significantly, this has been demonstrated in anoperational SEM. Speedups of 4× and more have been accomplished.

Further details of embodiments of the systems and methods describedherein are provided in the publication Hyrum S. Anderson, et al, “Sparseimaging for fast electron microscopy,” Proceedings of the SPIE, Vol.8657, id. 86570C 12 pp. (2013), which is incorporated herein byreference for all purposes.

Additional features and advantages are described herein, and will beapparent from the following Detailed Description and the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic drawing of an embodiment of a scanning electronmicroscope (SEM).

FIG. 2 shows an exemplary method for conducting electron or scanningprobe microscopy.

FIG. 2A shows an exemplary method for conducting a calibration for anelectron or scanning probe microscope.

FIG. 3 is an SEM monograph of Amorphophallus titanium pollen (left),with simulated 50% undersampling (center), and a reconstruction usingblock-DCT as a sparsifying basis (right).

FIG. 4 shows an exemplary electron microscope imaging system.

FIG. 5 shows an exemplary computing device that can be used inaccordance with the systems and methodologies disclosed herein isillustrated.

FIG. 6 is a histogram of the sparsity of the Dartmouth public electronmicroscopy images.

FIG. 7 is a series of graphs comparing basis pursuit imagereconstruction and bilinear interpolation image reconstruction both withand without noise.

FIG. 8 is a series of SEM micrographs: (top row) an original section ofa high-SNR micrograph from the SEM analysis of a particle atop thesurface Gibeon meteorite slice; (2nd row) simulated 10% sparse samples(left) and reconstruction (right); (3rd row) simulated 30% sparsesamples (left) and reconstruction (right); (4th row) simulated 50%sparse samples (left) and reconstruction (right).

FIG. 9 is: (top row) a standard SEM image of the Gibeon sample; (2ndrow) a 10% sparse (M/N=10%), modeled sample locations (left) andreconstruction (right); (3rd row) a 30% sparse, modeled sample locations(left) and reconstruction (right); (4th row) a 50% sparse, modeledsample locations (left) and reconstruction (right).

FIG. 10 shows: (panel i) a measurement of the scan coils dynamicresponse as a slow scan was performed; (panel ii) a measurement of thebeam being stepped from one extreme of the scan range to the other whilerecording from the secondary electron detector; (panel iii) thepositions of the landmarks plotted relative to each other to obtain datapoints along the step response curve.

FIG. 11 is a plot of collection time vs. M/N (%) for actual andtheoretical measured image acquisition times for collecting every pixelof a 1000×1000 image.

DETAILED DESCRIPTION

Systems and methods for electron and scanning probe microscope imagingare provided herein. Because SEMs are innately single-detector scanningsystems, the time to acquire thousands of images of tissue or materialfor analysis can be extremely prohibitive for many applications. In ageneral embodiment, the present disclosure provides a system and method(demonstrated on an operational SEM) for a sparse sampling scheme thatleverages image smoothness for compressed sensing inversion. Accurateknowledge of the probe location is utilized, and is accounted forthrough a linear dynamical model.

A scanning electron microscope (SEM) is an example of an electronmicroscope. FIG. 1 shows a simplified schematic view of an SEM. The SEMincludes a column 10 that houses several components. An electron gun 20that emits an electron beam 30 is disposed at an end of the column 10.One or more scan coils 40 are disposed along the interior of the column10, and these function to deflect the electron beam 30 onto a samplearea 50, thereby controlling where the beam contacts the sample area 50.During data gathering operations, the sample area 50 includes a sample60 disposed thereon for analysis. At least a portion of the sample area50 and sample 60 are divided into pixel locations that may be describedand x and y coordinates on a two-dimensional grid.

Components of the column 10 including the electron gun 20 and the coil40 are coupled to a computing device 90. The computing device 90 isfurther described below in reference to FIG. 5.

It is to be understood that this is a simplified description of an SEMthat is provided for explanatory purposes of the components andmethodologies described herein in greater detail. Other commoncomponents are not shown, such as detectors, a power source, condenserlenses and apertures, and an air lock and pump for the sample chamber,but their locations and function are to be understood.

In a scanning probe microscope embodiment, a physical probe (such as aneedle), rather than an electron beam, scans across the sample areasurface. There are other differences between electron and scanning probemicroscopes, which will be readily appreciated.

Other examples of electron microscopes include transition electronmicroscopes (TEM), reflection electron microscopes (REM), scanningoptical microscope (SOM), and scanning transmission electron microscopes(STEM). In another embodiment, the method is applicable to other domainsof nanometer microscopy in which speed is a limiting factor, includingscanning probe microscopy, such as atomic force microscopes (AFM) andscanning tunneling microscopes (STM).

FIGS. 2 and 2A illustrate exemplary methodologies relating to electronand scanning probe microscopy. While these methodologies are shown anddescribed as being a series of acts that are performed in a sequence, itis to be understood and appreciated that the methodologies are notlimited by the order of the sequence. For example, some acts can occurin a different order than what is described herein. In addition, an actcan occur concurrently with another act. Further, in some instances, notall acts may be required to implement a methodology described herein.

Moreover, the acts described herein may be computer-executableinstructions that can be implemented by one or more processors and/orstored on a computer-readable medium or media. The computer-executableinstructions may, for example, include a routine, a sub-routine,programs, and/or a thread of execution. Still further, results of actsof the methodologies may, for example, be stored in a computer-readablemedium and/or displayed on a display device.

Referring now to FIG. 2, a methodology 200 that facilitates electron orscanning probe microscopy is illustrated. The methodology 200 begins at210, and at 215 an electron beam or probe is driven to scan across asample and visit a subset of pixel locations of the sample that arerandomly or pseudo-randomly designated. The random sampling may, forexample, be computed by a processor in real-time and stored or thesampling may be directed by pre-computed random values. In anembodiment, the full set of pixel locations comprises the sample areathat is occupied by the sample itself. The number of pixel locations fora given sample area may be preset or determined by an operator, withinthe resolution limits of the particular microscope. Typically, the probeinteraction area on a sample is much smaller than the distance betweenpixel locations.

In an embodiment, the dwell time is variable at each location and is afunction of the random selection of pixels. Alternatively, the dwelltimes can be set to a given value required for achieving a desiredsignal-to-noise ratio (SNR). In general, the methodology 200 does notrequire increased dwell times to substantially maintain SNR, nor does itrequire decreased dwell times to provide the speed up in analysis.

In an embodiment, the dwell time is set, for example, 0.1 to 100microseconds, such as 1 microsecond to 10 microseconds or 3 microsecondsto 8 microseconds at each pixel location. Depending on the instrumentused and other settings, the selected dwell time may equate to 1 to 100samples at each random selected pixel location, such as 5 to 50 samples,or 10 to 25 samples. In an embodiment, the beam or probe continuouslysamples as it is in transit to the next pixel location. The result isthat the dwell time for a selected pixel or the number of samples perpixel are actually distributed across multiple pixel locations as theelectron beam or probe is in transit to the next pixel location of therandomly selected subset. It is a challenge, however, to know the actuallocation of the probe in transit while the sampling is performed. Thismay be determined however as explained below.

The random or pseudo random sampling of step 215 is in contrast totraditional electron microscope methodologies, where imaging rates arephysically constrained because the probe (probe meaning an electron beamor physical probe structure) visits each pixel location in raster-scanorder. As the probe or electrons in the incident beam interact with thesample, various signals are produced providing information about thecomposition or topography of the sample surface. These signals aredetected and digitally assigned to the image pixel value at thecorresponding sample location. The electron probe is then repositioned,for example, via electromagnetic or electrostatic deflection to asubsequent pixel location.

In an embodiment, the scanning speed of the beam or probe, that is thespeed at which the beam moves from one pixel to the next, is increasedby at least 1.5 times faster than the typical microscope setting, forexample, 2 times faster to 12 times faster, or 3 times faster to 5 timesfaster. For example, the beam or probe may have a scan speed of from0.05 pixels/microsecond to 100 pixels/microsecond, such as 10nm/microsecond to 50 nm/microsecond, or 60 nm/microsecond to 90nm/microsecond.

In an embodiment, rather than scanning each pixel location of thesample, the electron probe is commanded to visit a smaller subset ofpixel locations, for example, 10% to 50%, 30% to 50%, or 15% to 40% ofthe sample locations. A speed up in total analysis time will be realizedproportionately to the sample locations. For example, a 2× speed-upcorresponds to an analysis of a 50% subset of pixels and a 10× speed-upcorresponds to analysis of 10% of the pixel locations. If a sample hashigh contrast and/or large areas that are the same, it is morecompressible. Accordingly, in such samples a lower subset of pixels canbe analyzed and a higher speed up can be obtained.

In an embodiment, the electron beam or probe may be commanded to visitor sample one half or fewer of the total number of pixel locations of asample area, for example, one-third to one-tenth or one fourth toone-sixth of the total number of pixel locations.

The locations visited, although random or pseudo-randomly selected, may,for example, be visited in an order that follows the typical movement ofthe microscope beam or probe, such as vertical or horizontal rasterorder.

In an embodiment, the electron beam or probe is moved around the sampleby providing a set of voltage signals to the scan coils. These voltagesignals differ from the traditional signals that command the beam orprobe to move around the sample in raster order. Rather, the voltagesignals are varied to direct the beam or probe to provide the random orpseudo-random pattern of visitation and analysis.

In an embodiment, a hardware or software component acts as a randomizerto modify the driving of the probe or beam. For example, the componentcould be a computer or a custom ASIC or FPGA that sends a signal to themicroscope. In an embodiment, a control algorithm drives hardware tocreate voltage patterns and those voltage patterns are transmitted tothe scan coils of the microscope. In a small integrated systemembodiment, random voltage pattern codes could be pre-stored and builtinto the hardware system.

In an embodiment, the driving of the beam or probe can be combined witha mechanical mechanism to move the sample itself in relation to the beamor probe. In an embodiment, the electrical and mechanical movement canbe integrated with the beam or probe movement to examine a large sample.For example, once the full scope of the subset of pixels of the normalsample area is randomly analyzed by the beam or probe, a stage on whichthe sample is set may be mechanically moved to put an adjacent sectionof the sample in the scope of the beam or probe for further randomsampling.

Turning again to FIG. 2, the methodology 200 continues at step 220,which comprises determining actual pixel locations on the sample thatare visited by the electron beam or probe.

Part of the challenge encountered with only randomly sampling as opposedto sampling every location in raster-scan order is that it may bedifficult to know where the exact actual sampling locations are, andthis uncertainty makes it difficult to accurately reconstruct the image.This is particularly true where the sampling is distributed over severallocations while the beam or probe is scanning. This is not a problemwith conventional full pixel set raster scanning where there iscontinued motion in one direction at a constant speed. Inraster-scanning this is accounted for by starting the beam moving in onedirection and when it reaches a constant speed, only then does datacollection begin. Thus, the beginning of each row of the sample area isnot collected or analyzed. By going at a constant speed and spending aset dwell time at every consecutive pixel there is no need for adetailed model of how the beam dynamics work.

However, in the sparse imaging methodology 200 utilized withelectromagnetically driven beams or probes, the interval betweenrandomly-selected pixel locations within a scan line is highly variable,so that the effect of the dynamics is pronounced, and the measuredlocation may differ greatly from the desired location. Any time there isa change in the motion, there is a nonlinear response by the beam. In anSEM embodiment, the beam is deflected with two or more sets ofelectromagnetic coils, at least one for each scan direction. The currentdriven through these coils creates a magnetic field that deflects themoving electrons as they travel down the column. In addition to theinductance in the coils, stray capacitance and wire resistance creates adynamic system which cannot respond instantaneously to changes incurrent. Additionally, the amplifiers used to drive the coils exhibit anon-negligible dynamic response. The combination of these systemscreates a non-trivial dynamic system that can affect signals withfrequency content as low as tens or hundreds of kHz. As a result, theactual location of the beam is often not the same as the commandedlocation, which creates image distortion unless some compensation isdone.

Certain systems, such as electrostatic coil SEMs, do not typicallysuffer from the nonlinear response issues of electromagnetically drivensystems. Accordingly the determining step may be straightforward in suchsystems, that is, the expected location will equate to the actuallocation, and the determining step may be skipped.

In an embodiment, in order to determine actual pixel locations on thesample that are visited by the electron beam or probe, a calibrationstep is performed for calibrating the microscope to account for beamdynamics. The calibration is performed to predict where the beamactually is at a given point in time during transit of the beam. Ingeneral, the information on where the beam is commanded to be isrecorded, the actual measurement of a known sample at that point isdetected and recorded, and then using that information, an index iscreated to determine the actual pixel location that is being visited andanalyzed by the detector as a function of time. In an embodiment, thecalibration may be performed at a variety of magnifications and speeds.

The index created is employed in the determining step 220 to modify thecommanded location of the beam to correspond to the actual pixellocation of the beam when a given measurement is taken. The determiningmay be done in real time, during the sample analysis, or after thesample analysis is complete.

In an embodiment, determining of the actual location is based on atleast a 5th-order dynamical model shown in Equation (1).

$\begin{matrix}{\frac{\mathbb{d}^{5}{x(t)}}{\mathbb{d}t^{5}} = {{\alpha_{0}\left( {{\hat{x}(t)} - {x(t)}} \right)} - {\alpha_{1}\frac{\mathbb{d}{x(t)}}{\mathbb{d}t}} - {\alpha_{2}\frac{\mathbb{d}^{2}{x(t)}}{\mathbb{d}t^{2}}} - {\alpha_{3}\frac{\mathbb{d}^{3}{x(t)}}{\mathbb{d}t^{3}}} - {\alpha_{4}\frac{\mathbb{d}^{4}{x(t)}}{\mathbb{d}t^{4}}}}} & (1)\end{matrix}$where x(t) is the true one-dimensional probe position (in pixels) attime t, {circumflex over (X)}(t) is the desired position, and {a₀, . . ., a₄} are the best-fit parameters. To predict the actual location of theelectron probe, a ⅘ Runge-Kutta method may be used to solve Equation(1). An example of the processing step on an actual SEM sparse sampleddata is included below in the Examples section, which includes specificvalues for the best-fit parameters.

At step 235 of the methodology 200 shown in FIG. 2, processing of thedata collected by the microscope detectors from the visits of theelectron beam or probe at the actual pixel locations is performed, andthrough this, the reconstructed image of the sample is recovered.

In an embodiment, the image is reconstructed from the sparse pixel datathrough interpolation plus denoising using block-DCT with totalvariation regularizer. These calculations are described in detail below.The degrees of freedom of typical electron microscope images are manyfewer than the number of image pixels. Foundational contributions incompressed sensing guarantee that an N-pixel image x, which can bedescribed by K coefficients in some compression basis Ψ, can be exactlyrecovered in only M=O(K log N/K) linear measurements of the form y=Φx.The tightest guarantee to date holds when A=ΦΨ satisfies the restrictedisometry property, which guarantees recovery using basis pursuit:

${\min\limits_{x}{{{\Psi^{T}x}}1}} + {{\bigtriangledown\; x}}_{1}$s.t.y − Φ x ≤ σ²

It should be noted that for arbitrary A, certifying that the restrictedisometry property holds is combinatoric in M. Although mutual coherenceμ(ΦΨ) provides a looser guarantee on reconstruction from M=0 (μKlogN))measurements, it is trivial to compute.

In view of this, in an embodiment, noise and compression of the sparsesample data may be dealt with by the following approach. After M<Nmeasurements are collected (M=O(μKlogN) and N is the number of imagepixels), regularized basis pursuit denoising is performed to recover theimage from the compressed random sampling data. It is assumed that eachmeasurement is corrupted by white noise with noise power σ2. It isassumed that each measurement is corrupted by white noise with noisepower σ². A measurement model, based on sparsely sampled elementsy=Φx+n, may be used, where n is the additive noise with E[nn^(T)]=σ²I, Φrepresents a randomly selected subset of pixels (subset of rows ofidentity), and I is the identity matrix.

From the M<N measurements, the image can be reconstructed via

$\begin{matrix}{{{\min\limits_{x}{{{\Psi^{T}x}}1}} + {{\bigtriangledown\; x}}_{1}}{{s.t.{{y - {\Phi\; x}}}} \leq \sigma^{2}}} & (2)\end{matrix}$Where the compression basis, Ψ is chosen to be block-DCT in this casewith 32×32 pixel blocks. Block DCT may be chosen because it providesgood compressibility of SEM images and has low mutual coherence with thesampling scheme. The total-variation regularizer

∇x

1 is equal to (3):Σ_(i)√{square root over (|(∇_(h)x)_(i)|²+|(∇_(u)x)_(i)|²)}{square rootover (|(∇_(h)x)_(i)|²+|(∇_(u)x)_(i)|²)}  (3)and is employed to denoise the image and to promote smoothness betweenblock boundaries in the block-DCT.

Equation (2) can be solved by applying a basis pursuit recoveryalgorithm utilizing compressibility of the acquired image data forrecovering the reconstructed image. For example, this may beaccomplished through the split Bregman method by T. Goldstein and S.Osher, described in “The Split Bregman Method for L1-regularizedProblems,” SIAM Journal on Imaging Sciences 2(2), 323-343 (2009)(Goldstein and Osher), which is incorporated herein by reference. Byusing the Bregman iteration, the solution of the unconstrained problemwill converge to the solution of the constrained problem in (2) byiteratively solving for an intermediate solution to the problem, thenupdating the so-called Bregman parameters, which add the error back in.The equations and method below are exemplary.

${\min\limits_{x}{{{\Psi^{T}x}}1}} + {{\bigtriangledown\; x}}_{1} + {\frac{\mu}{2}{{y - {\Phi\; x}}}_{2}^{2}\mspace{14mu}\left( {{unconstrained}\mspace{14mu}{problem}} \right)}$

The compressed sensing MRI derivation in Goldstein and Osher can befollowed, noting that the present problem structure differs sinceimage-domain samples are collected rather than Fourier-domain samples.The split Bregman formulation is applied so that the problem can besolved iteratively to arbitrary precision. In particular, at the kthiteration, the following equation may be solved:

$\begin{matrix}{{{\min\limits_{x,u,v,w}{w}_{1}} + {\left( {u,v} \right)}_{2} + {\frac{\mu}{2}{{{\Phi\; x} - y}}_{2}^{2}} + {\frac{\lambda}{2}{{u - {\bigtriangledown_{u}x} - b_{u}^{k}}}_{2}^{2}} + {\frac{\lambda}{2}{{v - {\bigtriangledown_{v}x} - b_{v}^{k}}}_{2}^{2}} + {\frac{\gamma}{2}{{w - {\Psi^{T}x} - b_{w}^{k}}}_{2}^{2}}},} & (4)\end{matrix}$where w=Ψ^(T)x, u=∇_(u)x (horizontal gradient), v=∇_(v)x (verticalgradient) and shorthand∥(u,v)∥₂=Σ_(i)√{square root over (|u _(i)|² +|v _(i)|²)}.  (5)The so-called Bregman parameters are then updated via the threeequations below.b _(u) ^(k+1) =b _(u) ^(k)+(∇_(u) x ^(k+1) −u ^(k+1))  (6)b _(v) ^(k+1) =b _(u) ^(k)+(∇_(v) x ^(k+1) −v ^(k+1))  (7)b _(w) ^(k+1) =b _(w) ^(k)+(x ^(k+1) −u ^(k+1))  (8)The auxiliary variables w, u, and v, represent the DCT coefficients, thehorizontal gradient, and the vertical gradient, respectively, of theimage. The merit in the “split” Bregman formulation is that the I₁ andI₂ portions have been decoupled, allowing a simple solution viaalternating minimizations using element-wise shrinkage. See theequations below:

$u_{i}^{k + 1} = {\frac{\max\left( {{s_{i}^{k} - \frac{1}{\lambda}},0} \right)}{s_{i}^{k}}\left( {\left( {\bigtriangledown_{u}x^{k}} \right)_{i} + b_{u,i}^{k}} \right)}$$v_{i}^{k + 1} = {\frac{\max\left( {{s_{i}^{k} - \frac{1}{\lambda}},0} \right)}{s_{i}^{k}}\left( {\left( {\bigtriangledown_{v}x^{k}} \right)_{i} + b_{v,i}^{k}} \right)}$$w_{i}^{k + 1} = {{{shrink}\left( {{\left( {\Psi^{T}x^{k + 1}} \right)_{i} + b_{w,i}^{k}},\frac{1}{\gamma}} \right)}\mspace{14mu}{where}}$$s_{i}^{k} = {\sqrt{{{\left( {\bigtriangledown_{u}x^{k}} \right)_{i} + u_{i}^{k}}}^{2} + {{\left( {\bigtriangledown_{v}x^{h}} \right)_{i} + v_{i}^{k}}}^{2}}\mspace{14mu}{and}}$shrink(x, ρ) = sgn(x)max (x − ρ, 0).To solve (4) for x, however, one approach is to use a system ofequations that includes a circulant (μΦTΦ) plus diagonal (λΔ+γI). Forexample, solving (4) for xk+1 yields:(μΦ^(T) Φ−λΔ+γI)x ^(k+1)=μΦ^(T) y+λ∇ _(u) ^(T)(u ^(k) −b _(u))+λ∇_(u)^(T)(v ^(k) −b _(v))+γΨ(w ^(k) −b _(w)),  (9)This assumes that ΨTΨ, and uses Δ=−∇T∇ to represent the discreteLaplacian operator. Note that unlike the MRI example introduced inGoldstein and Osher, the system in (5) is not circulant since ΦTΦ isnon-constant along its main diagonal. Therefore, the system cannot bediagonalized by the discrete Fourier transform to arrive at an exactsolution. Nevertheless, as noted in Goldstein and Osher, an approximatesolution to x^(k) at each iteration suffices, since extra precision iswasted in the Bregman parameter update step. A few steps of theconjugate gradient method may suffice for arbitrary Φ, but for thespecial case in which Φ is a subset of the rows of identity, a moreefficient approach was utilized. Indeed, it was found that the algorithmconverges when approximating Φ^(T)Φ as the nearest circulant matrix C,where nearness is measured in terms of the Frobenius norm

ΦTΦ−C

F. This results in ΦTΦ≈C=aI, where a is the average of the elementsalong the main diagonal of ΦTΦ. The approximation error is bounded by

ΦTΦ−aI

F=√N/2 at M=N/2. Employing the circulant approximation allows (9) to besolved efficiently using Fourier diagonalization.

An alternative method of solving includes the conjugate gradient method.However, by approximating the system as circulant, and solving for xusing Fourier diagonalization, the overall algorithm converges, eventhough this step only provides an approximate solution. The basispursuit denoising implementation is essentially jointly interpolatingand denoising from the undersampled image data.

In summary, the above application of the split Bregman formulation forbasis pursuit interpolation includes an inner loop that solves (2) via(6)-(8) and a circulant approximation to (5), and an outer loop thatupdates the Bregman parameters via (3)-(5). For typical images on theinterval[0, 1], it was found that μ=λ=1 and γ=10−2 are reasonable valuesfor reconstruction. In the implementation herein, two iterations of theinner loop, and 150 iterations of the outer loop for noiseless data wereused, though 20-50 iterations are typically sufficient to producehigh-quality reconstructions.

Once the processing and recovering step 235 is completed or at leastpartially completed, the processed and recovered image or partial imageis displayed in a displaying step 240. For example, the image may bedisplayed through an output device, such as a monitor or printer. Themethodology 200 completes at 245.

With reference to FIG. 2A, an exemplary methodology 250 for performingthe above-referenced calibration is illustrated. The methodology 250begins at 255, and at 260, in order to model the dynamics of the system,including the effects of the amplifiers and scan coils of the system, astepwise jump in position from one extreme of the beam's scanning rangeto the other over a calibration sample is commanded. For example, thetwo extremes may be at opposite extremes in a horizontal row across thecalibration sample. At 265, while the electron beam is in transit acrossthe sample, the output of the secondary electron detector is recorded.At 270, this step-scanning routine produces a “smeared” scan of thesample. At 275, a standard slow raster scan of the same sample isperformed across the same extremes of the sample. The beam in the twoscans is run in the same direction, for example, horizontallyleft-to-right. At 280, a comparison of the “smeared” scan and the slowraster scan is performed. At 285, using the comparison data, the transitof the beam is plotted as a function of time to create an index thatreflects the beam dynamics. (See also Example 5 below).

FIG. 3 shows an example reconstruction from M=N/2 randomly selectedsamples of an excised 512×512 block from an SEM monograph ofAmorphophallus titanium pollen (left panel). The center panel shows asimulated 50% random undersampling. The right panel shows areconstruction using the above processing method with block-DCT as asparsifying basis (PSNR is 36 dB).

The sparse imaging methodology 200 is capable of achieving efficientdata collection at the expense of greater off-line computation.Moreover, the methodology 200 may still require an order of magnitudemore time to reconstruct the image than was required to collect thedata. The greater computation times may be acceptable, since, incontrast to data collection, image recovery may be distributed acrossmany CPUs.

Referring now to FIG. 4, in an embodiment, the computing device 490includes or is coupled to a processor 410 and a computer-readable memory420 (which may be memory or a data store) that comprises a plurality ofcomponents that are executed by the processor 410. The computing device90 can be configured to execute the methodology 200 described herein.

A command component 430 is configured to command an electron beam orprobe to scan across a sample area and visit a subset of desired pixellocations of the sample area. The subset of desired pixel locations maybe designated in a random or pseudo-random manner. A determinercomponent 440 is configured to determine actual pixel locations on thesample area that are visited by the electron beam, and a reconstructioncomponent 450 is configured to process data collected by detectors fromthe visits of the electron beam at the actual pixel locations andrecover a reconstructed image from the processed data.

In an embodiment, the computing device 90 is part of a system thatincludes input and output devices, and in an embodiment, thefunctionalities of one or more of the components, particularly thereconstruction component 450, are executed across a distributed seriesof multiple processors.

In an embodiment, the computing device 90 comprises a small electronicshardware package that includes components to do analog to digitalconversion and digital to analog conversion, and a processing unit tocontrol the values. Software to execute the sparse sampling methodology200, may be either implemented on the hardware package or on a remotecomputer that is connected to the hardware package. The remote computer,for example, may perform the data processing or just the computationalintensive tasks associated with the iterative reconstruction process. Inan embodiment, the computing device comprises electronics hardware forgenerating random or pseudo-random sampling patterns.

In an embodiment, the methodology 200 may be implemented as software ona computing device that is coupled to an electron or scanning probemicroscope and also executes instructions for operating the microscope.

Referring now to FIG. 5, a high-level illustration of an exemplarycomputing device 500 that can be used in accordance with the systems andmethodologies disclosed herein is illustrated. The computing device 500includes at least one processor 502 that executes instructions that arestored in a memory 504. The instructions may be, for instance,instructions for implementing functionality described as being carriedout by one or more components discussed above or instructions forimplementing one or more of the methods described above. The processor502 may access the memory 504 by way of a system bus 506. In addition tostoring executable instructions, the memory 504 may also, for example,store random or pseudo randomly selected pixel locations or voltages fordriving a beam to such pixel locations, data received from the detectorsof the electron or scanning probe microscope, and algorithms used inexecuting the determining and processing steps mentioned above.

The computing device 500 additionally includes a data store 508 that isaccessible by the processor 502 by way of the system bus 506. The datastore 508 may include, for example, executable instructions, random orpseudo randomly selected pixel locations or voltages for driving a beamto such pixel locations, data received from the detectors of theelectron or scanning probe microscope, and algorithms used in executingthe determining and processing steps mentioned above. The computingdevice 500 also includes an input interface 510 that allows externaldevices to communicate with the computing device 500. For instance, theinput interface 510 may be used to receive instructions from an externalcomputer device, from a user, etc. The computing device 500 alsoincludes an output interface 512 that interfaces the computing device500 with one or more external devices. For example, the computing device500 may display text, images, etc. by way of the output interface 512.

It is contemplated that the external devices that communicate with thecomputing device 500 via the input interface 510 and the outputinterface 512 can be included in an environment that providessubstantially any type of user interface with which a user can interact.Examples of user interface types include graphical user interfaces,natural user interfaces, and so forth. For instance, a graphical userinterface may accept input from a user employing input device(s) such asa keyboard, mouse, remote control, or the like and provide output on anoutput device such as a display. Further, a natural user interface mayenable a user to interact with the computing device 500 in a manner freefrom constraints imposed by input device such as keyboards, mice, remotecontrols, and the like. Rather, a natural user interface can rely onspeech recognition, touch and stylus recognition, gesture recognitionboth on screen and adjacent to the screen, air gestures, head and eyetracking, voice and speech, vision, touch, gestures, machineintelligence, and so forth.

Additionally, while illustrated as a single system, it is to beunderstood that the computing device 500 may be a distributed system.Thus, for instance, several devices may be in communication by way of anetwork connection and may collectively perform tasks described as beingperformed by the computing device 500.

Various functions described herein can be implemented in hardware,software, or any combination thereof. If implemented in software, thefunctions can be stored on or transmitted over as one or moreinstructions or code on a computer-readable medium. Computer-readablemedia includes computer-readable storage media. A computer-readablestorage media can be any available storage media that can be accessed bya computer. By way of example, and not limitation, suchcomputer-readable storage media can comprise RAM, ROM, EEPROM, CD-ROM orother optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to carry or storedesired program code in the form of instructions or data structures andthat can be accessed by a computer. Disk and disc, as used herein,include compact disc (CD), laser disc, optical disc, digital versatiledisc (DVD), floppy disk, and Blu-ray disc (BD), where disks usuallyreproduce data magnetically and discs usually reproduce data opticallywith lasers. Further, a propagated signal is not included within thescope of computer-readable storage media. Computer-readable media alsoincludes communication media including any medium that facilitatestransfer of a computer program from one place to another. A connection,for instance, can be a communication medium. For example, if thesoftware is transmitted from a website, server, or other remote sourceusing a coaxial cable, fiber optic cable, twisted pair, digitalsubscriber line (DSL), or wireless technologies such as infrared, radio,and microwave, then the coaxial cable, fiber optic cable, twisted pair,DSL, or wireless technologies such as infrared, radio and microwave areincluded in the definition of communication medium. Combinations of theabove should also be included within the scope of computer-readablemedia.

Alternatively, or in addition, the functionally described herein can beperformed, at least in part, by one or more hardware logic components.For example, and without limitation, illustrative types of hardwarelogic components that can be used include Field-programmable Gate Arrays(FPGAs), Program-specific Integrated Circuits (ASICs), Program-specificStandard Products (ASSPs), System-on-a-chip systems (SOCs), ComplexProgrammable Logic Devices (CPLDs), etc.

EXAMPLES

By way of example and not limitation, the following examples areillustrative of various embodiments of the present disclosure.

The sparse sampling method was demonstrated with public domain SEMimages and on an operational SEM. As shown in the Examples below,acceptable image quality was achieved at 3× speedup. This wasaccomplished by commanding the electron probe to visit arandomly-selected subset of pixel locations, predicting the actuallocations via a 5th-order dynamical model, then recovering the imageusing a split-Bregman formulation of regularized basis pursuit thatleveraged block-DCT as a compression basis.

Example 1

To assess image sparsity of typical electron microscopy images, 1,022electron microscopy images (SEM, TEM and E-SEM) were obtained from theDartmouth public domain gallery. The images are of a variety ofdifferent specimens in biology, geology, and materials, and include awide range of magnifications and image sizes. To standardize analysis,the center 512×512 of each image was excised to remove banners andrescaled images to [0; 1] grayscale values. For each 512×512 image, thesparsity K was computed by counting the number of large coefficients inthe block-DCT domain (32×32 blocks) that accounted for at least 99.75%of the total coefficient energy.

FIG. 6 shows a histogram of the sparsity of the Dartmouth publicelectron microscopy images, where sparsity is measured by counting thenumber of block-DCT coefficients K that account for at least 99.75% ofthe image energy. The average sparsity is 17%, with half of all imagesless than 15% sparse, and three-quarters less than 20% sparse.

This suggests that by applying compressed sensing, most SEM images couldbe acquired with compressed measurements with about 20-40% reduction inthe number of samples, with little or no information loss.

Example 2

Using the proposed recovery method in equation (1) (see above),reconstruction of the public domain Dartmouth images analyzed in Example1 was simulated from sparse samples. For each 512×512 excised andstandardized image x, sparse sampling was simulated by choosing M pixelsat random from the image, where M/N is swept from 10% to 100%. Then, theimages were reconstructed using both the basis pursuit approach andbilinear interpolation approach described above for comparison purposes.

FIG. 7 shows the results of this comparison. The top panels showcalculations without noise, and the bottom panels were calculated withintroduced noise. (Noise was multiplicative: for pixel intensity η, zeromean white Gaussian noise was added with variance η/100).

The shading at each x/y location on the plot indicates how frequently animage with a given sparsity K/N was “successfully” reconstructed(accounted for at least 99.75% of the image energy) at a givenundersampling rate M/N; the shading ranges from 0% (black) to 100%(white). The reconstructed image x^ was deemed a “success” if thefollowing inequality were true:∥x−{circumflex over (x)}∥ ₂ ² /∥x∥ ₂ ²≦0.25%

In other words, if the reconstruction accounts for at least 99.75% ofthe image energy, the image was “successfully” recovered.

It can be seen from the plots on the top panels, for noiselessreconstruction, basis pursuit and bilinear interpolation areapproximately the same, with the phase transition between success andfailure on the bilinear interpolation curve accounting for about 5% lessarea under the curve. However, when a very small amount of noise isadded (multiplicative noise, in the case with variance 1/100 of thepixel intensity), bilinear interpolation breaks down quickly, with 50%less area under the curve compared to the basis pursuit denoisingmethod.

Simple linear interpolation of the sparse sampled compressed images isboth simple and very efficient. For example, the reconstruction in FIG.3 (pollen sample), the basis pursuit approach took 18 seconds for 50iterations using non-optimized MATLAB code with a 2.66 GHz Intel Xeonprocessor, whereas a similar reconstruction using MATLAB's griddata forlinear interpolation took only 2 seconds. Thus, linear interpolation maybe attractive as a “quick-look” option, but the proposed basis pursuitdenoising method is preferred for high-quality reconstruction.

Example 3

Example 3 demonstrates on an operational SEM, the sparse sampling andrecovery method for fast electron microscopy. The experiments wereconducted using a commercially available SEM column with customelectronics to drive the beam location and sample the detector. A ZeissGmbH (Oberkocken, Germany) column was used with a Schottky thermal fieldemission source and Gemini™ optics. A nominal beam energy of 10 keV wasused with a 10 μm aperture, resulting in a beam current of approximately200 pA.

The incident beam was deflected onto the sample using the standardscanning coils and current amplifiers in the column. However, customelectronics were used to set the desired beam location using an externalscan mode. The magnification (and consequently the field of view) wasset using the standard column controls. Once this was determined, pixelsin the field of view were visited by driving a voltage of −10 V to +10V, which is converted to a current in the coil amplifiers. For example,in the horizontal direction, driving −10 V would place the beam at thefar left of the field of view and +10 V would place the beam at the farright. The same is true in the vertical direction.

A digital to analog converter (DAC) was used to drive the desiredvoltages by converting an digital signal from the computer to an analogsignal that controls the scan coils. The detector was sampled using ananalog to digital converter (A/D) that was synchronized to the DAC. TheA/D and DAC were implemented using a National Instruments (Austin, Tex.)PCI-6110 multi-function data acquisition system. This system has amaximum frequency of 2.5 MHz with two analog outputs, an outputresolution of 16 bits per sample and an input resolution of 12 bits persample. DACs generally have a maximum “sample rate” at which they canupdate their command signals. This maximum rate can be considered one“sample.” The amount of dwell time at any pixel must be an integermultiple of this sample time. Thus, if the beam was desired to dwelllonger than the minimum sample time at one point, the DAC is commandedto hold a voltage for multiple samples. The effective dwell time (moredwell time means better SNR for that pixel) was then controlled by howmany multiples of the basic sample time that the DAC was commanded tohold at each point. In this Example, variable dwell time was achieved bydigitally averaging multiple samples at the same pixel location. A basicdwell time of 400 ns using one sample per pixel resulted in low-signalto noise ratio (SNR) images, while a high-SNR dwell time of 6.4 μs wasachieved by averaging 16 samples per pixel.

A high-SNR image of the surface of a Gibeon meteorite collected in themanner just described is shown in FIG. 8, along with simulated sparsesampling and subsequent image recovery.

A digital command is created in a computer and this gets converted by aDAC to an analog signal that controls the scan coils. DACs generallyhave a maximum “sample rate” at which they can update their commandsignals. This maximum rate can be considered one “sample”. The amount ofdwell time at any pixel must be an integer multiple of this sample time.If we want the beam to dwell longer than the minimum sample time at onepoint, we command the DAC to hold a voltage for multiple samples. Theeffective dwell time (more dwell time means better SNR for that pixelbecause we average all the samples) is then controlled by how manymultiples of the basic sample time we command the DAC to hold at eachpoint.

FIG. 8 shows: (top row) an original section of a high-SNR micrographfrom the SEM analysis of a particle atop the surface Gibeon meteoriteslice; (2nd row) simulated 10% sparse samples (left) and reconstruction(right); (3rd row) simulated 30% sparse samples (left) andreconstruction (right); (4th row) simulated 50% sparse samples (left)and reconstruction (right).

It should be noted that on an operational SEM, nontrivial dynamics ofthe electron probe scanning system create a mismatch between the desiredand actual measurement locations on the sample. The effect is lesspronounced when visiting every pixel in typical raster-scan mode inwhich the electron probe follows the same trajectory during each scanline, and leads only to a nonlinear stretch of the image. However, asexplained above, in the sparse imaging embodiment, the interval betweenrandomly-selected pixel locations within a scan line is highly variable,so that the effect of the dynamics is pronounced, and the measuredlocation differs greatly from the desired location.

Example 4

In Example 4, the sparse sampling method was utilized in an operationalSEM. Mirroring Example 3, the electron probe was commanded to visit 10%,30% and 50% of the sample locations chosen at random in vertical-rasterorder, and to dwell for 6.4 μs (16 samples per pixel) at each randomlyselected pixel location. The result is that the 16 samples per randomlyselected pixel are actually distributed across multiple pixel locationsas the electron probe is in transit. To predict the actual location ofthe electron probe, a ⅘ Runge-Kutta method to solve Equation (1).

A portion of the Gibeon meteorite sample was imaged at 800×magnification at a working distance of 4.7 mm. Due to the close workingdistance, samples were collected with an in-lens secondary electron (SE)detector. Brightness and contrast for each sparse sampling collectionwas fixed at 76% and 41%, respectively.

Results for the sparse sampling collection and reconstruction are shownin FIG. 9, which shows: (top row) a standard SEM image of the Gibeonsample; (2nd row) a 10% sparse (M/N=10%), modeled sample locations(left) and reconstruction (right); (3rd row) a 30% sparse, modeledsample locations (left) and reconstruction (right); (4th row) a 50%sparse, modeled sample locations (left) and reconstruction (right). Theintensity of the gray-scale in the left column represents the number oftimes the probe visited the given pixel. The electron probe scannedvertically. In addition to sample quality, a difference in samplecharging is also evident, which indicates that the sparse samplingmethod may be additionally useful for samples that are sensitive tooverdosing.

For M/N=10%, the reconstruction exhibits some smearing along thevertical path of the electron probe, which can be attributed to largeelectron probe velocities and small errors in the 5th order model actuallocation prediction. Acceptable image reconstruction is achieved forM/N=30%, corresponding to a greater than 3× increase in image collectionspeed. Notice also that for smaller M/N, the lower average electron doserates contribute to less charging on the sample (manifest by the slightglow on the left-hand side of the original image).

Example 5

A calibration routine was performed to characterize the dynamics of theamplifiers and scan coils. This was done by commanding a stepwise jumpin position from one extreme of the beam's scanning range to the otherover a calibration sample. While the electron beam was in transit, theoutput of the secondary electron detector was recorded. Thisstep-scanning method produced a smeared scan of the sample.

Comparing this with a very slow raster scan of the same sample allowedplotting a beam location corresponding to the recorded output of thedetector as a function of time.

FIG. 10 shows a measurement of the scan coil's dynamic response. Paneli) shows a measurement of the scan coils dynamic response as a slow scanwas performed to obtain a nearly dynamics-free image of the sample. Inpanel ii) the beam was stepped from one extreme of the scan range to theother while recording from the secondary electron detector. This fastscan resulted in a smeared or distorted image. Landmarks (A, B, and C)on both images were located, and then an approximate step response (plotin iii) was extracted that shows where the beam actually was at eachpoint in time. The vertical axis of (iii) is beam location (horizontallyin i and ii) and the horizontal axis is time. The beam was commanded tomove from the bottom of the figure (left side of the image) to the top(right side) instantaneously, so the plotted curve represents how closethe actual position was to the commanded position as a function of time.

The data showed the dynamics of the beam are slow compared to thesampling period (400 ns). The 90% rise time was approximately 12 μs, the99% rise time about 32 μs, and the 99.9% rise time approximately ¼ ms.Note that the 99.9% rise time is relevant; when making scans of severalthousand pixels per line, an error of 0.1% corresponds to severalpixels.

The lowest order linear model to fit the data points well wasfifth-order of the form of equation (1) where x(t) is the trueone-dimensional probe position (in pixels) at time t, {circumflex over(x)}(t) is the desired position, and the best-fit parameters {a₀, . . ., a₄} are listed in Table 1. The same dynamical model was used for bothhorizontal and vertical beam deflection.

TABLE 1 parameter value α₀ 4.42 × 10⁻⁴ α₁ 8.20 × 10⁻³ α₂ 5.49 × 10⁻² α₃2.46 × 10⁻¹ α₄ 4.60 × 10⁻¹

Example 6

The measured image acquisition time for collecting every pixel of a1000×1000 image with 16 samples per pixel was determined to be 6.9 s. Animage acquisition time of 6.4 s was expected at 2.5 MHz. Using sparsesampling factors of 10%, 30% and 50%, image collection times of 0.7 s(9.9× speedup), 2.1 s (3.3× speedup), and 3.5 s (2.0× speedup),respectively, for 1000×1000 images. These collection times were onlyslightly more than what would be predicted at 2.5 MHz, and this can beascribed to software overhead. Nevertheless, the collection time indeedgrows linearly with the number of samples M, as shown in FIG. 11.

As used herein, the terms “component” and “system” are intended toencompass computer-readable data storage that is configured withcomputer-executable instructions that cause certain functionality to beperformed when executed by a processor. The computer-executableinstructions may include a routine, a function, or the like. It is alsoto be understood that a component or system may be localized on a singledevice or distributed across several devices. Additionally, as usedherein, the term “exemplary” is intended to mean serving as anillustration or example of something, and is not intended to indicate apreference. The term “random” when used by itself herein may includeboth random and pseudo-random as those terms are technically defined inthe art.

All patents, patent applications, publications, technical and/orscholarly articles, and other references cited or referred to herein arein their entirety incorporated herein by reference to the extent allowedby law. The discussion of those references is intended merely tosummarize the assertions made therein. No admission is made that anysuch patents, patent applications, publications or references, or anyportion thereof, are relevant, material, or prior art. The right tochallenge the accuracy and pertinence of any assertion of such patents,patent applications, publications, and other references as relevant,material, or prior art is specifically reserved.

In the description above, for the purposes of explanation, numerousspecific details have been set forth in order to provide a thoroughunderstanding of the embodiments. It will be apparent however, to oneskilled in the art, that one or more other embodiments may be practicedwithout some of these specific details. The particular embodimentsdescribed are not provided to limit the invention but to illustrate it.The scope of the invention is not to be determined by the specificexamples provided above but only by the claims below. In otherinstances, well-known structures, devices, and operations have beenshown in block diagram form or without detail in order to avoidobscuring the understanding of the description. Where consideredappropriate, reference numerals or terminal portions of referencenumerals have been repeated among the figures to indicate correspondingor analogous elements, which may optionally have similarcharacteristics.

It should also be appreciated that reference throughout thisspecification to “one embodiment”, “an embodiment”, “one or moreembodiments”, or “different embodiments”, for example, means that aparticular feature may be included in the practice of the invention.Similarly, it should be appreciated that in the description variousfeatures are sometimes grouped together in a single embodiment, figure,or description thereof for the purpose of streamlining the disclosureand aiding in the understanding of various inventive aspects. Thismethod of disclosure, however, is not to be interpreted as reflecting anintention that the invention requires more features than are expresslyrecited in each claim. Rather, as the following claims reflect,inventive aspects may lie in less than all features of a singledisclosed embodiment. Thus, the claims following the DetailedDescription are hereby expressly incorporated into this DetailedDescription, with each claim standing on its own as a separateembodiment of the invention.

What is claimed is:
 1. A method for conducting electron or scanningprobe microscopy, the method comprising: driving an electron beam orprobe to scan across a sample and visit a subset of pixel locations ofthe sample that are randomly or pseudo-randomly designated; determiningactual pixel locations on the sample that are visited by the electronbeam or probe; and processing data collected by detectors from thevisits of the electron beam or probe at the actual pixel locations andrecovering a reconstructed image of the sample.
 2. The method of claim1, wherein the driving of the electron beam is performed byelectrostatic or electromagnetic scan coils.
 3. The method of claim 2,wherein the determining of the actual pixel locations is based onresults of modeling dynamics of the scan coils.
 4. The method of claim3, further comprising modeling the dynamics of the scan coils by:commanding a stepwise jump in position from one extreme of an electronbeam or probe scan range to a second extreme in a calibration routine;during the stepwise jump of the electron beam or probe, recording outputof a detector; comparing the recorded output of the detector with outputrecorded during a raster scan of the calibration sample; and plotting abeam location corresponding to the recorded output of the detector as afunction of time.
 5. The method of claim 3, wherein the modelingdynamics is based on at least a 5th-order dynamical model of the scancoils to determine the actual location of the probe or beam as afunction of time.
 6. The method of claim 1, wherein the desired pixellocations are not the same as the actual pixel locations.
 7. The methodof claim 1, wherein the electron beam or probe is drivenelectromagnetically or electrostatically.
 8. The method of claim 1,further comprising recovering the reconstructed image of the sample byusing a basis pursuit recovery algorithm utilizing compressibility ofthe acquired data for recovering the reconstructed image.
 9. The methodof claim 1, wherein the beam or probe continuously samples as it is intransit to a next pixel location of the subset of pixel locations. 10.The method of claim 1, wherein the samples are distributed acrossmultiple pixel locations as the beam or probe is in transit to a nextpixel location of the subset of pixel locations.
 11. The method of claim1, wherein the sample is sensitive to overdosing.
 12. An electronmicroscope imaging system comprising: a processor; and acomputer-readable memory that comprises a plurality of components thatare executed by the processor, the plurality of components comprising: acommand component configured to command an electron beam or probe toscan across a sample area and visit a subset of pixel locations of thesample area, the subset of pixel locations being randomly orpseudo-randomly designated; a determiner component configured todetermine actual pixel locations on the sample area that are visited bythe electron beam or probe; and a reconstruction component configured toprocess data collected by detectors from the visits of the electron beamor probe at the actual pixel locations and recover a reconstructed imagefrom the processed data.
 13. The electron microscope imaging system ofclaim 12, wherein the reconstruction component is executed by adistributed series of processors.
 14. The electron microscope imagingsystem of claim 12, wherein the command component instructs the electronbeam or probe to sample one half or fewer pixel locations.
 15. Theelectron microscope imaging system of claim 12, wherein thereconstruction component is configured to recover the reconstructedimage of the sample by using a basis pursuit recovery algorithmutilizing compressibility of the acquired data for recovering thereconstructed image.
 16. The electron microscope imaging system of claim12, wherein the command component is configured to command the beam orprobe to continuously sample as the beam or probe is in transit to anext pixel location of the subset of pixel locations.
 17. The electronmicroscope imaging system of claim 12, wherein the command component isconfigured to sample across multiple pixel locations as the beam orprobe is in transit to a next pixel location of the subset of pixellocations.
 18. An electronic microscope comprising: an electron gun thatemits an electron beam; scan coils that deflect the electron beam; asample area comprising pixel locations; a processor, wherein theprocessor drives the scan coils to deflect the electron beam onto thepixel locations; and a computer-readable memory that comprises aplurality of components that are executed by the processor, theplurality of components comprising: a command component configured tocommand an electron beam or probe to scan across a sample area and visita subset of pixel locations of the sample area, the subset of pixellocations being randomly or pseudo-randomly designated; a determinercomponent configured to determine actual pixel locations on the samplearea that are visited by the electron beam or probe; and areconstruction component configured to process data collected bydetectors from the visits of the electron beam or probe at the actualpixel locations and recover a reconstructed image from the processeddata.
 19. The electron microscope of claim 18, wherein thereconstruction component is configured to recover the reconstructedimage of the sample by using a basis pursuit recovery algorithmutilizing compressibility of the acquired data for recovering thereconstructed image.
 20. The electron microscope of claim 18, whereinthe command component is configured to sample across multiple pixellocations as the beam or probe is in transit to a next pixel location ofthe subset of pixel location.